On the Complexity of Maximizing Social Welfare within Fair Allocations of Indivisible Goods

We consider the classical fair division problem which studies how to allocate resources fairly and efficiently. We give a complete landscape on the computational complexity and approximability of maximizing the social welfare within (1) envy-free up to any item (EFX) and (2) envy-free up to one item (EF1) allocations of indivisible goods for both normalized and unnormalized valuations.

@article{bu2025_2205.14296,
  title={ Approximability Landscape of Welfare Maximization within Fair Allocations },
  author={ Xiaolin Bu and Zihao Li and Shengxin Liu and Jiaxin Song and Biaoshuai Tao },
  journal={arXiv preprint arXiv:2205.14296},
  year={ 2025 }
}